Theorems · Theorem · group theory
AddCommute.isAddUnit_add_iff
∀ {M : Type u_1} [inst : AddMonoid M] {a b : M}, AddCommute a b → (IsAddUnit (a + b) ↔ IsAddUnit a ∧ IsAddUnit b)- Defined in
- Mathlib.Algebra.Group.Commute.Units
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- AddUnitsproof · cited by 325
- AddUnits.valproof · cited by 248
- IsAddUnitstatement and proof · cited by 215
- AddCommutestatement and proof · cited by 185
- AddUnits.isAddUnitproof · cited by 14
- IsAddUnit.addproof · cited by 11
- AddUnits.leftOfAddproof · cited by 1
- AddUnits.rightOfAddproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- isAddUnit_add_self_iffproof · cited by 0